[Pw_forum] elastic constants and internal strain

[Eduardo Ariel Menendez Proupin]

Hi all,

As far as I understand, PWSCF calculates the stress following Nielsen and
Martin, PRL 50, 697 (1985), with expressions updated for ultrasoft
pseudopotentials and maybe other thechnical upgrades. In the formalism of
Nielsen and Martin, the stress is calculated as a partial derivative of the
energy versus the strain tensor, hence keeping frozen the atomic
coordinates. The effect of keeping frosen the atomic fractional coordinates
have a large effect in the paradigmatic case of the C44 elastic modulus of
silicon, where there is a large internal strain when the cristal is strained
along the [111] direction. In the times of 1985, the internal strain
contribution to the stress was evaluated using more theory and the (I guess,
experimental) values of the TO phonon frequency.

In modern times, I would instead relax the atomos in the strained cell, and
take the value of the stress tensor at the relaxed geometry. Doing so, I
think I still lose
part of the stress, related with the derivative of the atomic positions with
respect to the strain.  On the other hand, the internal strain can be
accounted for, calculating the elastic moduli from the second derivative of
the energy with respect to the strain.

I tested both methods to obtain the C44 constant of silicon, using the
strain long the [111] direction. With both methods I obtain the same value
of 77.1 GPa. I expected to obtain different values. What am I missing?

 I checked that not allowing relaxation, I also obtained the same value for
the C44(0) using the energy and the stress data. I also checked that the
constant C11 give consistent values.


-- 
Eduardo Menendez
Departamento de Fisica
Facultad de Ciencias
Universidad de Chile
Phone: (56)(2)9787439
URL: http://fisica.ciencias.uchile.cl/~emenendez
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